Solving this relaxation leads to a solution that is potentially infeasible. Specifically, certain positions (\(i\)  in \(x_{it}\) ) may have no car class assigned and other positions may have two or more cars assigned. To rectify this infeasibility, Lagrangian multipliers (\(\lambda \) ) are introduced, which penalise positions in the sequence where either zero or more than one car have been assigned. The multipliers are modified via subgradient optimisation [1]}, which aims to find the “ideal” set of multipliers over a number of iterations. ACO [2]} is incorporated within Lagrangian relaxation [id=AE]as a repair method leading to the LRACO heuristic. The flowchart of the LRACO method is shown in Fig. REF  and its pseudocode and associated details are presented in Appendix A.
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